Calibrating and compensating influence of casing thickness variations on measurements of low frequency A.C. magnetic fields within cased boreholes to determine properties of geological formations

ABSTRACT

This invention relates to the measurement of the longitudinal components of low frequency A.C. magnetic fields from within cased boreholes which are used to measure geophysical properties of geological formations. The applied A.C. magnetic fields are generated by passing low frequency A.C. current through insulated wires or by conducting low frequency A.C. current through geological formations, either of which are examples of conducting A.C. currents through different &#34;circuit pathways&#34;. The currents generating the applied A.C. magnetic fields are in the frequency range between 0.001 Hz and 20 Hz. The measured longitudinal components of the resulting total A.C. magnetic fields within the cased boreholes are responsive to various geophysical parameters which include the resistivities of the portions of the geological formations subject to said applied A.C. magnetic fields and to thickness variations of the casing. Calibration methods and apparatus reduce the influence of the unwanted effects due to thickness variations of the casing.

This application is a continuation-in-part application of Ser. No.07/474,930, filed Feb. 5, 1990, which is to issue as U.S. Pat. No.5,065,100 on Nov. 12, 1991 that is entitled "Measurement of In-Phase andOut-of-Phase Components of Low Frequency A.C. Magnetic Fields WithinCased Boreholes to Measure Geophysical Properties of GeologicalFormations". Ser. No. 07/474,930 is a continuation-in-part applicationof Ser. No. 07/200,573, filed on May 31, 1988, which issued as U.S. Pat.No. 4,901,023 on Feb. 13, 1990 that is entitled "Methods and Apparatusfor Measurement of Low Frequency A.C. Magnetic Fields Within CasedBoreholes to Determine Properties of Geological Formations" portions ofwhich were disclosed in U.S. Disclosure Document No. 189,963 with filingdate of Apr. 4, 1988 and U.S. Disclosure Document No. 256,866 withfiling date of Jul. 2, 1990. Ser. No. 07/200,573 is acontinuation-in-part application of Ser. No. 06/857,160, filed on Apr.29, 1986, which issued as U.S. Pat. No. 4,748,415 on May 31, 1988 thatis entitled "Methods and Apparatus for Induction Logging In CasedBoreholes, a portion of which was disclosed in U.S. Disclosure DocumentNo. 127,101 filed on May 2, 1984.

A search of Class 324, Subclass 339 provides in excess of 100 U.S.Patents concerned with induction logging of open hole formations.Typical of the methods and apparatus for open hole induction logging aredisclosed in the following U.S. Pat. Nos. 4,513,376; 4,499,421;4,455,529; 4,278,941; 3,706,025; 3,051,892; and 2,220,070. However,these disclosures do not present adequate methods and apparatus tofunction within borehole casing.

A search of Class 324, Subclass 368 provides many U.S. Patents concernedwith electrical measurements in the presence of borehole casing. Typicalmeasurements involved passing current through the casing and into theformation as disclosed in the following U.S. Pat. Nos. 2,891,215;2,729,784; 2,587,518; 2,459,196; and 2,414,194. However, these methodsand apparatus do not provide magnetic sensing means for measurementsthrough casing.

Heretofore, it has been impossible to perform induction logging typemeasurements inside borehole casing to measure the resistivity ofadjacent geological formations. One reason for this is that the responseof a typical logging tool depends linearly on the conductivity ofadjacent formation volumes, and varies inversely as the radius to thatvolume to the 6th power (Electrical Methods in Geophysical Prospecting,by George V. Keller and Frank C. Frischknecht, Pergamon Press, New York,Equation 58, page 82). The borehole casing is not only close to theinduction coils but it is much more conductive than adjacent formations.Therefore, the signal from the casing dominates the signal from theformation. And furthermore, variations in the thickness of the casingdue to oxidation effects, etc., produce systematic differences in thedata which are larger than the formation signal in prior devices.Therefore, prior devices have not provided a means to nullify therelatively large signal coming from the casing to allow the measurementof the formation response.

In addition, the magnetic steel casing has a "skin depth" δ at aparticular frequency given by the following equation:

    δ=(ρ/πfμ).sup.1/2                          Eq. 1

(Please refer to Fields and Waves in Communication Electronics, by SimonRamo, et. al., John Wiley & Sons, New York, Second Edition, 1984,Equation 11 on page 149.) Here ρ is the resistivity, f is the frequencyand μ is the magnetic permeability of the pipe. The magnetic fields aredampened exponentially with the skin depth. Typical steel pipes haveresistivities of 10⁻⁷ ohm-meters, and relative permeabilities of 100, sothat the skin depth equals the thickness of a 1/2 inch thick pipe at afrequency of 1.6 Hz. The high relative permeability of steel boreholecasing allows it to be called "magnetic steel borehole casing".Therefore, since the applied A.C. magnetic field in the induction systemmust penetrate the walls of the casing to the surrounding earth,frequencies of 20 Hz and lower must be used for such measurements.Heretofore, much higher frequencies have been used in open hole systems.Such low frequencies required in a cased hole, however, require a verysensitive induction coil magnetometer which is responsive to lowfrequency A.C. magnetic fields inside magnetic steel borehole casing.Therefore, an improved down hole induction coil magnetometer is requiredfor formation resistivity measurements.

The through-casing induction coil magnetometers must be very sensitiveto weak A.C. magnetic fields produced by currents caused to flow information. However, it is known that the natural geomagnetic noiseproduces fluctuations in the earth's magnetic field, and in thebandwidth between .001 Hz to 20 Hz, the peak-to-peak variations of saidgeomagnetic noise exceed 1×10⁻⁵ gauss peak-to-peak. Heretofore, suchnoise has provided a natural limit to the measurability of A.C. magneticfields. However, A.C. magnetic fields from the induced flowing currentsin the earth may be smaller than this magnitude of noise. The inventionprovides a differential magnetometer, or gradiometer, which allowsmeasurements of A.C. magnetic fields much smaller than the geomagneticnoise present. And furthermore, the invention provides apparatus andmethods which allow operation of said sensitive A.C. magneticgradiometer inside conductive and magnetic steel borehole casing.

And finally, since the steel borehole casing is also magnetic having arelative permeability of approximately 100, the magnetic fields fromflowing currents in the vicinity of the borehole casing becomesubstantially distorted by the presence of the casing. Magnetic fieldswhich are perpendicular to the casing are magnetically shielded from theinterior of the casing by the cylindrically shaped magnetic casingitself. A.C. magnetic fields which are parallel to the casing, orlongitudinal fields, penetrate the casing to a degree depending on thefrequency, the geometry of the casing, the conductivity of the casing,and the magnetic permeability of the casing. At low enough frequencies,such as 1 Hz, appreciable longitudinal components of said A.C. magneticfields penetrate the casing without any special provisions, a fact whichhas not been generally recognized in the prior art. However, all otherfactors being a constant, the relatively high magnetic permeability ofthe casing tends to concentrate the magnetic field lines inside thecasing. To avoid such problems, the invention also provides magneticsensors which are themselves comprised of relatively massiveconcentrations of highly magnetic materials which dominate the presenceof the casing and allow the measurement of weak A.C. magnetic fieldsthrough magnetic borehole casing.

Sources of magnetic fields, or the "primary excitation fields", whichare located within the interior of a cased well bore interact with thesurrounding casing and rock formation in complex ways. In thedescription of this problem, cylindrical coordinates are naturally used.The excitation field may be resolved at any point within the formationinto a longitudinal component which is parallel to the casing, a radialor perpendicular component to the casing, and an azimuthal componentwhich is orthogonal to the other directions. In general, for radialcomponents of the excitation field, these components do not penetrate tothe exterior of the casing at D.C. or at any frequency because of thefamiliar magnetic shielding arguments. At D.C. and low frequencies,longitudinal components of the excitation field may penetrate thecasing, provided eddy current losses in the casing are not too great atthe frequency of interest. And finally, for a short length casing,azimuthal excitation fields are transparent to the casing under certaincircumstances because of the nearly lossless generation of circulatingsurface currents which are made to flow continuously on the interior andexterior surfaces of the casing. For long lengths of casing, however,the azimuthal fields are attenuated by eddy currents.

Therefore, the primary excitation A.C. magnetic fields within the casingmay produce longitudinal and azimuthal components of the A.C. magneticfields on the exterior of the casing. These exterior A.C. magneticfields in turn cause induced currents to flow within the formation, asis the case with standard induction logging. These secondary currentsthen produce secondary A.C. magnetic fields which in turn interact withthe casing in a complex fashion. Here, too, the longitudinal andazimuthal components of the secondary fields penetrate the casing undercertain circumstances. These secondary fields may be measured fromwithin the interior of the casing with various magnetic sensing meanswhich provide an indication of the nature of the formation, and inparticular, the resistivity of the formation.

Accordingly, an object of the invention is to provide new inductionlogging methods for formation identification through borehole casing.

It is yet another object of the invention to provide new and practicalinduction logging apparatus for formation identification throughborehole casing.

And further, it is another object of the invention to provide newmagnetic methods for formation identification through borehole casing.

And still further, it is another object of the invention to provide newmagnetic sensing apparatus for formation identification through boreholecasing.

FIG. 1 is a section view of a preferred embodiment of the invention forinduction logging in the presence of borehole casing.

FIG. 2 is a plot of B_(in) /B_(out) vs. frequency for longitudinal A.C.magnetic fields applied to the exterior of a length of borehole casing.

FIG. 3 is a plot of B_(out) /B_(in) vs. frequency for an azimuthal fieldapplied to the interior of several different lengths of borehole casingsby a current carrying insulated wire.

FIG. 4 is a generalized conceptual drawing showing the cylindricalcomponents of the primary A.C. magnetic field (the excitation field),the resulting currents flowing in formation, the surface currentsflowing on the casing, and the secondary magnetic fields generated bythe flowing currents.

FIG. 5 is another embodiment of the invention wherein the source of theexciting field is derived by passing A.C. current through formation.

FIG. 6 is another embodiment of the invention wherein the sources of theexciting fields are A.C. current carrying loops of insulated wire on thesurface of the earth which are concentric with the casing.

FIG. 7 is another embodiment of the invention wherein the sources of theexciting fields are two A.C. current carrying loops of insulated wire onthe surface of the earth, one of which is concentric with the casing,and the other of which is located a horizontal distance away from saidcasing.

FIG. 8 is another embodiment of the invention wherein measurements ofthe longitudinal components of the A.C. magnetic field are performed ina first cased borehole in response to A.C. magnetic fields generatedwithin a second cased borehole.

FIG. 9 is another embodiment of the invention wherein measurements ofthe longitudinal components of the A.C. magnetic field are made in afirst cased borehole in response to current conducted from an electrodeattached to the top of the casing of the first cased borehole to anelectrode in electrical contact with the interior of a second casedborehole.

FIG. 1 shows a preferred embodiment of the apparatus for inductionlogging within borehole casing 10 which surrounds the borehole itself.The formation has resistivities of p₁, and p₂. High permeabilitymaterials 12 and 14 respectively are surrounded with windings 16 and 18respectively which provide two independent sources of the primaryexcitation A.C. magnetic fields, solenoids S1 and S2 respectively. Thehigh permeability materials 12 and 14 respectively are constructed frommu-metal and a typical material is Permalloy 80 manufactured byMagnetics, Inc., located in Butler, Pa. The cores are approximately 1inch by 1 inch square, being comprised of several stacks of long thinmu-metal strips each of which is 0.014 inch thick, 1/2 inch wide and 4foot long. Approximately 200 turns of insulated #18 copper wire are usedto fabricate windings 16 and 18 respectively. A programmable oscillator20, which may be set to different frequencies and voltage amplitudes,provides the input to a power amplifier 22 which provides a high powerA.C. voltage and current source to programmable switch 24 which is anelectronic switch. Power amplifier 22 typically provides A.C. current atfrequencies from 0.001 Hz to 20 Hz and currents of several ampspeak-to-peak which is sufficient to generate A.C. magnetic fields of atleast several gauss peak-to-peak in the immediate vicinity of solenoidsS1 and S2. Wire 26 is connected to both common sides of the coils 12 and14 respectively. The programmable switch initially energizes S1 when theoutput of the power amplifier is connected to wire 28 and theprogrammable switch subsequently energizes S2 when the power amplifieris connected to wire 30. Programmable switch 24 therefore alternatelyenergizes S1 and S2 for fixed periods of time T each.

High permeability materials 32, 34, and 36 respectively are surroundedby insulated windings 38, 40, and 42 respectively which comprise threeseparate induction coils I1, I2, and I3. High permeability materialmagnetic traps 44, 46, and 48 improve the performance of the inductioncoils in the presence of the casing. (For additional information on suchmagnetic traps, please refer to the U.S. Pat. No. 4,656,422 entitled"Oil Well Logging Tools Measuring Paramagnetic Logging Effect for Use inOpen Boreholes and Cased Well Bores", which issued on Apr. 7, 1987,having inventors W. B. Vail and P. B. Schwinberg, with a filing date ofApr. 8, 1985, which is Ser. No. 720,943.) Each of the induction coilsare resonated at identical center frequencies with capacitors C₁, C₂,and C₃ respectively. In addition, the resistors R₁, R₂, and R₃ trim thefrequency responses of the induction coils so that they are identical.Amplifiers A1, A2, and A3 amplify each voltage present providing threeseparate voltage outputs from the induction coil sensors, V₁, V₂, andV₃.

The induction coils I1, I2, I3, are typically 6 foot long to achieve theoverall required sensitivity. The cores 32, 34, and 36 are approximately6 foot long, and are 1 inch by 1 inch square, being comprised of severalstacks of long thin mu-metal strips each of which is 0.014 inch thick,1/2 inch wide and 6 foot long. This provides a sensor whose length is atleast ten times longer than any other lateral dimension of the core.This is important because long slender cores efficiently attractmagnetic field lines (Electrical Methods in Geophysical Prospecting, op.cit., page 237). Each lamination is electrically isolated by either aplastic spray coat or an insulating oxide layer to minimize eddy currentlosses. Typical of suitable materials used in these cores is Permalloy80 type mu-metal manufactured by Magnetics, Inc. Approximately 30,000turns of #24 gauge insulated copper wire are wound on a coil form whichholds the laminations in a bundle. The mass of magnetic material in thecore of the induction coil encourages magnetic flux outside the casingto concentrate in the magnetic cores of the induction coils.

The high permeability magnetic traps 44, 46, and 48 are constructed ofthe same individual thin mu-metal laminations as are used in the coreand are disposed radially around the induction coils. The laminationsare each electrically isolated from one another. These traps areapproximately the same length as the induction coils and haveapproximately the same total combined mass as the cores.

In addition, the "magnetic weight" of a body may be defined as itsweight times the relative permeability of the medium to air. The casingtypically weights 20 lbs./ft. and has a relative permeability of 100 sothat its "magnetic weight" is 2,000 lbs./ft. The 1 inch by 1 inch coreshave a weight of 0.31 lbs./ft. but Permalloy 80 has a relativepermeability in excess of 100,000 at low frequencies thereby producing a"magnetic weight" of greater than 30,000 lbs./ft. for the core.Therefore, the sensor should have a "magnetic weight" which is equal toor greater than the "magnetic weight" of the casing for optimumresponse.

The magnetic traps 44, 46, and 48 improve the response of the inductioncoils, although they are not absolutely essential for operation. Thehighly magnetic cores of the induction coils will of course havefringing fields which interact the steel borehole casing. When theinduction coils are resonated at a particular frequency with one of thecapacitors C₁, C₂, or C₃, then these fringing fields interact stronglywith the wall of the casing which reduces the response of the coils bycausing eddy current losses in the casing. However, the traps 44, 46,and 48 respectively, tend to "trap" the fringing fields from the ends ofthe cores thereby keeping these fields from interacting with the casing.Those fringing fields do not cause losses in the magnetic trap since theindividual magnetic laminations of the trap are electrically isolatedfrom one another. Ideally, the weight of the trap should be comparableto the weight of the cores, although substantial variations will stillwork. And the lengths of the traps are ideally equal to the lengths ofthe cores but may be as short as one half as long to twice as long asthe core lengths for reasonable operation.

In addition, calibration coil 49 is disposed equidistant from inductioncoil I1 and induction coil I2. Similarly, calibration coil 50 isdisposed equidistant from induction coils I2 and I3. As explained inU.S. Pat. No. 4,656,422, these calibration coils are used to applyidentical A.C. magnetic fields to each induction coil pair (I1 and I2for example) when they are used in a differential manner. Thesecalibration coils are comprised of 10 turns of insulated #18 gaugecopper wire and are energized by simple circuitry which is not shown forsimplicity. Such coils provide A.C. magnetic balancing means for theA.C. magnetic gradiometer.

The output voltages V₁, V₂, and V₃ proceed to the programmabledifference electronics 51. Under command from the computer 52 over wire54, differences in voltages from the various induction coils may beelectronically provided as follows: V₁ -V₂ and V₂ -V₃. Electronics 51also provides filtering, amplitude adjustment, and phase adjustmentcircuitry. The voltage output of the difference electronics 51 proceedsover wire 56 to the phase sensitive detector 58. The phase sensitivedetector provides an in-phase output and an out-of-phase output withrespect to the oscillator reference signal provided to the phasesensitive detector by cable 60. The respective outputs of the phasesensitive detector are provided individually to the computer 52 fordigital averaging and data analysis.

The primary excitation sources S1 and S2 are separated by a distance Dand the three induction coils are also individually separated by thedistance D. The center line of the high permeability material 32 isseparated from the centerline of the high permeability material 14 bythe distance L. In addition, means not shown are provided to house thevarious elements in the borehole tool as accustomed in the industry, toprovide a wireline enclosing wires 26, 28, 30, 54, and 56, and toprovide logging truck hardware and standard instrumentation usedroutinely by the industry.

The first step in the operation of the induction tool is to choose theoperating frequency. Because the applied fields from the solenoids S1and S2 must penetrate the casing, frequencies lower than 20 Hz must beused to measure formation properties. The lower limit of response of theinduction coils is perhaps 0.001 Hz. Typically, 1 Hz will be chosen asthe operation frequency. Then calibration coil 49 is energized with a 1Hz signal (the circuitry necessary to do this is not shown forsimplicity). Then, calibration coil 49 applies an identical A.C.magnetic field to induction coils I1 and I2. Then C₁ is chosen forresonating the coils at 1 Hz and R₁ is chosen to be approximately 50Kwhich sets the frequency response of I1. Then C₂ and R₂ are chosen tocause a null in the output signal of differential unit 51. Then, I1 andI2 respond identically even if the borehole casing adjacent to each ofthe coils has a different thickness or average resistivity. In thiscondition, the A.C. magnetic gradiometer is said to be balanced. Thecalibration coils 49 and 50 are each balancing means in this case. Also,since noise fluctuations in the geomagnetic field are approximately thesame at induction coils I1, I2, and I3, the differential output of anypair of induction coils is substantially immune to the naturalgeomagnetic noise present!

When S1 is energized at the appropriate center frequency of theinduction coils, it produces primarily a longitudinal magnetic fieldparallel to the borehole casing adjacent to S1. For low frequencies,this A.C. magnetic field penetrates the casing which subsequently causesinduced eddy currents to flow in the geological formation in thevicinity of the borehole. The resulting flowing eddy currents cause anadditional secondary A.C. magnetic field contribution, dB1, which ismeasured by measuring the voltage difference V₁ -V₂. Similarly, when S2is alternatively energized, dB2 is measured by measuring V₂ -V₃.Differences between these two measurements [(V₁ -V₂)-(V₂ -V₃)] are dueentirely to differences in the resistivity of the formation over thevertical distance D, spurious casing contributions, and spurious fluidcontributions in the hole. However, such differences are not due todirect coupling to the sources S1 and S2 as is required for properoperation. Such differential measurements provide a gradient in theresistivity of the formation, along with other information. In addition,there is an interesting cross-check of the data using a verticaltranslation of the apparatus. Suppose that the apparatus is initially ina given vertical location and that solenoid S1 is used in conjunctionwith measurement induction coils I1 and I2 which results in ameasurement of V₂ -V₁. Since S1 and S2 are separated by the distance D,and I1, I2, and I3 are all separated by the distance D, then translatingthe apparatus vertically by the distance D should place the solenoid S2and induction coils I2 and I3 respectively adjacent to the sameformations initially measured. Therefore, measurements of V₃ -V₂ hereshould be equal to the initial measurements of V₂ -V₁.

Such gradient measurements on the formation may be provided at differentfrequencies provided computer control of C₁, C₂, and C₃ and R₁, R₂, andR₃ are provided appropriately. Both the frequency of the oscillator 20and its amplitude affect the degree of radial penetration of theformation. The spurious influence of pipe joints may be minimized if thedistance D is much larger than the thickness of typical pipe joints.Furthermore, pipe joints are periodic with the length of casing.Therefore, the data at different vertical positions may be Fouriertransformed with the period of the casing length, and this component maybe removed mathematically.

In addition, information may be obtained from energizing just onesource, S1 for example, and measuring the output from just one inductioncoil, V₁, at several different frequencies between 0.001 Hz and 20 Hz,for example. Under appropriate circumstances, the average resistivity ofthe formation may be determined adjacent to the borehole using thismethod.

FIG. 2 shows the longitudinal transfer characteristics (B_(inside)/B_(outside)) of an A.C. magnetic field applied to the outside of alength of borehole casing and subsequently measured on the interior ofthe casing. In these experiments a longitudinal A.C. magnetic field wasapplied to an 85 inch long length of 95/8 inch O.D. Type P110 boreholecasing, with a wall thickness of 0.475 inches, which was manufactured byNippon Steel, Inc. An air core induction coil was placed on the interiorof the casing for these measurements. Clearly, below 10 Hz, thesemeasurements prove that longitudinal A.C. magnetic fields substantiallypenetrate the casing. These measurements show why frequencies below 20Hz are used for measurements of longitudinal A.C. magnetic fieldsthrough borehole casing.

FIG. 3 shows the transfer characteristic (B_(out) /B_(in)) of anazimuthal field applied to the interior of a length of casing andsubsequently measured on the outside of the casing for a short length ofcasing and for a long length of casing respectively which are insulatedfrom the earth. A short length of casing is anything shorter than 100feet long and a long length of casing is anything longer than 1,000 feetlong. Here an insulated A.C. current carrying wire is placed insidevarious lengths of 7 inch O.D., 3/8 inch wall thickness, Type K-55casing manufactured by Valexy, Inc. The ratio of B_(out) /B_(in) isplotted for the azimuthal component of the A.C. magnetic field atvarious frequencies. Although the skin depth at the higher frequenciesis only a small fraction of the thickness of the wall of the casing,circulating surface currents flowing simultaneously on the inside andoutside of the pipe make the pipe effectively transparent to azimuthalfields for a short length of casing. For long lengths of casing, fieldsare strongly attenuated at frequencies above 20 Hz.

Each magnetic gradiometer is comprised of two balanced induction coils,such as I1 and I2, and can achieve remarkable measurement accuracyinside borehole casing. Without the traps 44 and 46, for example,measurement accuracies of 1×10⁻⁹ gauss peak-to-peak with integrationtimes of several seconds can be achieved. With the traps 44 and 46included, for example, measurement accuracies of 1×10⁻¹⁰ gausspeak-to-peak with integration times of several seconds can be achieved.These accuracies can be obtained in the presence of the noisy earth'sgeomagnetic field which has noise components of 1×10⁻⁵ gausspeak-to-peak between 1 Hz to 10 Hz! Depending on the strength of thesource S1 and S2, the A.C. magnetic fields due to flowing inducedcurrents may be in the 10⁻⁶ gauss peak-to-peak range. Therefore, use ofthis precision A.C. magnetic gradiometer would be helpful to elucidatethe resistivity of the geological formation under these circumstances.

It is possible to separate out the contributions from the primaryexcitation fields, the casing, and the formation resistivity by varyingthe frequency of the apparatus. If only the solenoid S1 is energized,and only induction coils I1 and I2 are used in a gradiometerarrangement, then the output of the gradiometer can be measured atseveral different frequencies, for example at 1 Hz and 20 Hz. At 1 Hz,the output of the gradiometer is a function of the primary excitationfield, the casing, and the resistivity of the formation. However, at 20Hz for example, the output is dependent only on the primary excitationfield and the casing but not on the resistivity of the formation becausethe primary excitation A.C. magnetic fields do not substantiallypenetrate the casing to the formation at 20 Hz. Similar sets ofmeasurements using the other solenoid S2 but the same induction coils I1and I2 then allows unique separation of the primary A.C. magnetic fieldsand the effects of the casing because the different vertical position ofS2 changes the primary A.C. fields measured by the gradiometerconsiderably. Therefore, the formation resistivity can be uniquelyobtained as desired. The process then can be repeated with inductioncoils I2 and I3.

FIG. 4 shows a conceptualized measurement situation inside a boreholecasing. A primary excitation source of A.C. magnetic field 58 produces ageneral longitudinal (B_(z)), radial (B_(r)), and azimuthal (B.sub.φ)components of the A.C. magnetic field at any position within theformation. The formation resistivity and other physical parameters are afunction of z, r, and φ. The primary source fields generate eddycurrents at any position of magnitude J_(z), J_(r), and J.sub.φ. Theseflowing currents then produce secondary fields b_(z), b_(r), andb.sub.φ. Along with the primary fields, these secondary fields aremeasured with longitudinal A.C. magnetic field sensors 60 and 62, whoserespective outputs are differentially processed by electronics 64.

In general, the radial components B_(r) do not penetrate the casing, andany components b_(r) produced will not be measurable inside the casing.The source field B_(z) can penetrate the casing at low frequencies, andthe secondary component b_(z) can be measured with induction coils aswas the case in FIG. 1. In FIG. 4, elements 60 and 62 are inductioncoils similar in nature to induction coils I1 and I2 described in FIG. 1which are sensitive to longitudinal components of the A.C. magneticfield on the interior of the borehole casing. The calibration coil 63 isused to balance the gradiometer as already described for FIG. 1.Difference electronics 64 in FIG. 4 differentially subtracts the signalsfrom induction coils 60 and 62 respectively and provides the output ofthe A.C. magnetic gradiometer. The magnetic gradiometer can be operatedat different frequencies as already described. In addition, usefulgeophysical information can also be obtained from using just oneinduction coil to measure the response to the excitation source which isoperated at several different frequencies between 0.001 Hz and 20 Hz.Such measurements are to be repeated at many different verticalpositions while keeping the distance of separation fixed between thesource and the one induction coil. Such a log provides informationresponsive to the casing and the adjacent geological formation. Providedthe data is averaged over suitable vertical distances, the influence ofthe casing may be minimized thereby yielding information concerning theadjacent geological formation as desired.

FIG. 5 shows yet another embodiment of the invention. Many of theelements have been defined, but here power amplifier 22 delivers A.C.current to electrode 66 placed in electrical contact with the casing.The current is subsequently conducted by various processes to electrode68 which is in electrical contact with the surface of the earth.Induction coils 70 and 72 are conceptually similar in nature toinduction coils I1 and I2 in FIG. 1 and are responsive to onlylongitudinal components of the A.C. magnetic field inside the boreholecasing. Calibration coil 73 is also shown which is used to balance theA.C. magnetic gradiometer. Here, A.C. currents which flow along thecasing do not cause a signal output of the gradiometer because suchcurrents do not produce magnetic fields with components parallel to thecasing. However, the A.C. currents which flow through formation tend toflow along relatively less resistive zones. Various resistive zones areshown in FIG. 5 with resistivities respectively ρ₁, ρ₂, and ρ₃. Forexample, if ρ₂ <ρ₁ then more current would flow through ρ₂ than throughρ₁. Such A.C. currents would produce A.C. magnetic fields withlongitudinal components inside the borehole casing and would thereforeproduce measurements indicating the relative resistivity of the adjacentformations. The difference in the outputs of the sensors performed byelectronics 64 is sensitive to formation resistivities in differentgeological layers shown as ρ₁, ρ₂, and ρ₃ in FIG. 5. Currents ofdifferent frequencies can be conducted through formation, and themagnetic gradiometer can be operated at the different frequencies asalready described. In addition, useful geophysical information may alsobe obtained from using just one induction coil to measure the responseto conducting A.C. currents through formation at various differentfrequencies between 0.001 Hz and 20 Hz. While keeping the distance ofseparation fixed between the source of the A.C. current applied to thecasing and the one sensing induction coil, such measurements are to berepeated at many different vertical positions. Such a log providesinformation responsive to the casing and the adjacent geologicalformation. Provided the data is averaged over suitable verticaldistances, the influence of the casing may be minimized thereby yieldinginformation concerning the adjacent geological formation as desired.

FIG. 6 shows a variant of the invention shown in FIG. 1. Here many ofthe elements have already been defined. As is the case in FIG. 1, threeinduction coil assemblies 74, 76, and 78 respectively are sensitive tothe secondary longitudinal magnetic fields sensed through the casing.However, the primary excitation A.C. magnetic fields are not generatedfrom inside the casing, but instead are due to turns of insulated wire80 and 82 respectively which are disposed on the surface of the earthand which are concentric with the borehole casing. However, the theoryof operation of the embodiment of the invention shown in FIG. 6 issimilar to that shown in FIG. 1. Wire 80 is typically 10 meters indiameter and capable of carrying at least 10 amps peak-to-peak, and wire82 is typically 20 meters in diameter and also capable of carrying 10amps peak-to-peak. The frequency of operation is typically 0.001 Hz to20 Hz to allow deep penetration of the earth, and to allow the A.C.magnetic fields to penetrate the casing. Calibration coils 84 and 86 areused to balance the appropriate pairs of the induction coils whenperforming differential measurements. First, wire 80 is energized, andinduction coils 74 and 76 are used in a differential manner. Then, wire82 is energized and induction coils 74 and 76 are still used in adifferential manner. Two independent measurements at the same verticalposition gives separately the formation and casing response. Inaddition, measurements at several different frequencies such as 0.01 Hz,1 Hz, and 10 Hz can be used to separate the casing and formationresponses. And finally, useful geophysical information may also beobtained from using just one induction coil to measure the response to asingle excitation source located on the surface of the earth which isoperated at the various different frequencies. Such measurements at thedifferent frequencies are to be repeated after placing the singleinduction coil at different vertical positions within the casedborehole. Such a log provides information responsive to the casing andthe adjacent geological formation. Provided the data is averaged oversuitable vertical distances, the influence of the casing may beminimized thereby yielding information concerning the geologicalformation as desired.

Several embodiments of the invention have been shown explicitly in FIGS.1, 4, 5 and 6. The embodiments of the invention described to this pointprovide at least the following four fundamental "Methods" which aremethods of measurement:

Method I: In the embodiments of the invention described to this point, alow frequency A.C. magnetic field is generated which is called theprimary source A.C. magnetic field. Said field can be generated by atleast several common means: A) passing A.C. current through conductivewires which are insulated from the earth; or B) passing A.C. currentthrough a combination of conductive wires which are insulated from theearth and in addition conducting said A.C. current through a portion ofthe earth as a part of the A.C. current conducting circuit; and C) lessconventional means not shown to this point including using mechanicalmodulation of permanent magnets and electromagnetic modulation ofpermanent magnets. (It is understood that said sources may be placed inmany different geometric configurations in the oil field and A.C.magnetic fields generated in many different ways as described at lengthbelow in the further analyses of the many subcategories of Methods I-Aand Methods I-B.)

Method II: In all of the embodiments of the invention described, thelongitudinal component of the low frequency A.C. magnetic field isdetected at a minimum of one vertical position from within the casedborehole to be measured which is to be called the "first cased borehole"during the remaining disclosure. The total longitudinal componentmeasured at any one vertical position within the first cased boreholecan be resolved into two components: the primary longitidinal componentdue to the primary source A.C. magnetic field; and the secondarylongitudinal component the A.C. magnetic field produced by eddy currentscaused to flow in the geological formation, in the casing, in any cementwhich may be present around the casing, and in the mud and fluids withinthe hole. Said eddy currents are responsive to the resistivities of theconductive media surrounding the longitudinal A.C. magnetic fielddetector. (Said secondary component in principle also includes all extracomponents added to the A.C. magnetic field which are generated inresponse to said primary source field. Extra components due to anynon-linear processes including rectification phenomena and otherphysical processes related to various electrochemical phenomenaassociated with conducting current through actual geological formationsadd vectorially to the secondary component of the A.C. magnetic fielddescribed). It is also recognized that various A.C. magnetic detectionmeans responsive to the longitudinal components of the A.C. magneticfield include the following: A) induction coils with ferromagneticcores; B) induction coils with air cores; C) induction coils withferromagnetic cores whose length is at least 10 times longer than anyother lateral dimension of the induction coil; D) induction coils withair cores whose length is at least 10 times longer than any otherlateral dimension of the induction coil; E) Hall effect devices orientedsuitably to be sensitive to the longitudinal components of the A.C.magnetic field; F) proton precession magnetometers which are modified tobe sensitive to the longitudinal components of the A.C. magnetic field;G) optical pumping magnetometers which are oriented suitably to measurelongitudinal components of the A.C. magnetic field; H) any type ofsemiconductor device which is sensitive to the longitudinal componentsof the A.C. magnetic field; and I) virtually any device which measuresthe longitudinal component of magnetic fields and which can be placedinside a borehole casing.

Method III: In all of the embodiments of the invention described to thispoint, the longitudinal A.C. magnetic field detection measurementmethodology may be characterized as one of the following: A) a singledetector measuring the magnitude of the longitudinal component of theA.C. magnetic field which is located at one vertical position within thefirst cased hole; B) two detectors measuring a differential outputresponsive to the difference between the magnitudes of the longitudinalcomponents of the A.C. magnetic fields which are present at the twodifferent vertical locations of the two detectors where all of saiddetectors are vertically disposed within said first cased borehole; C)two detectors measuring a differential output responsive to thedifference between the magnitudes of the longitudinal components of theA.C. magnetic fields which are present at the specific locations of thetwo detectors where at least one of said detectors is located within thefirst cased borehole and where said second detector may or may not belocated within said first cased borehole; D) three or more detectorsmeasuring differential outputs responsive to the differences between themagnitudes of the longitudinal components of the A.C. magnetic fields atthe many different vertical positions of said detectors within saidfirst cased borehole where all of said detectors are vertically disposedwithin said first cased borehole; E) three or more detectors measuringdifferential outputs responsive to the differences between themagnitudes of the longitudinal components of the A.C. magnetic fieldswhich are located at the many different locations where at least one ofsaid detectors is located within the first cased hole and where saidremaining detectors may or may not be located within said first casedborehole; and F) two or more detectors measuring differential outputsresponsive to the differences between the magnitudes of the longitudinalcomponents of the A.C. magnetic fields provided by the first detectorlocated in the first cased borehole and the total components of themagnetic fields appearing at the other detectors which may or may not belocated within said first cased borehole. Possible unspecified locationsfor the remaining detectors include the following locations: in thefirst cased borehole; in a second cased borehole; in an uncasedborehole; and on the surface of the earth, etc. It is understood,however, that in general, measurements of the longitudinal component ofthe A.C. magnetic field provided by the detector in the first casedborehole are generally to be repeated at many different verticalpositions thereby providing a "log" usually desired by the industry.

Method IV: In the embodiments described to this point, the longitudinalA.C. magnetic field may be measured at the following frequencies: A) atjust one frequency between 0.001 Hz and 20 Hz; and B) at two or moredifferent frequencies between 0.001 Hz and 20 Hz.

For the sake of brevity, the invention includes using in combination andpermutations of all the following individual Methods which comprise manyoverall detailed Procedures. Such Procedures are characterized by thefollowing choices: Method I-A or Method I-B or Method I-C; used incombination with Method II-A, or Method II-B, or Method II-C, or MethodII-D, or Method II-E, or Method II-F, or Method II-G, or Method II-H, orMethod II-I; used in combination with Method III-A, or Method III-B, orMethod III-C, or Method III-D, or Method III-E or Method III-F; and usedin combination with Method IV-A or Method IV-B.

In addition there are many different ways of passing current through theearth as defined in the general Method I-B above. In particular, it isuseful to present the many different experimental ways current is passedthrough the earth for the particular Procedure defined as follows:Method I-B, in combination with Method II-A, in combination with MethodIII-A, and in combination with Method IV-B. This particular Procedure isbriefly defined as follows: the primary excitation source is to passcurrent through the earth; the A.C. magnetic field is to be measuredwith an induction coil which has a ferromagnetic core; a single detectoris to provide measurements in said first cased borehole; andmeasurements are to be performed at two or more frequencies between0.001 Hz and 20 Hz.

However, it is still necessary to describe how the current is to bepassed through the earth for specificity here. Listing said differentways to pass current through the formation for this particular Procedurealso defines the various subcategories of Method I-B in general whichare listed as follows:

Method I-B (1): passing A.C. current from one electrode in electricalcontact with the interior of the first cased borehole to one electrodelocated on the surface of the earth and which is in electrical contactwith the surface of the earth.

Method I-B (2): passing A.C. current from one or more electrodes inelectrical contact with the interior of the first cased borehole to oneor more electrodes located on the surface of the earth and which are inelectrical contact with the surface of the earth.

Method I-B (3): passing A.C. current from one electrode in electricalcontact with the interior of the first cased borehole to one electrodeattached to and in electrical contact with the portion of said firstcasing which protrudes above the surface of the earth.

Method I-B (4): passing A.C. current from one or more electrodes inelectrical contact with the interior of the first cased borehole to oneor more electrodes attached to and in electrical contact with theportion of said casing which protrudes above the surface of the earth.

Method I-B (5): passing A.C. current from one electrode in electricalcontact with the interior of the first cased borehole to one electrodewhich is in electrical contact with the interior of a second casedborehole.

Method I-B (6): passing A.C. current from one or more electrodes inelectrical contact with the interior of the first cased borehole to oneor more electrodes which are in electrical contact with the interior ofa second cased borehole.

Method I-B (7): passing A.C. current from one electrode in electricalcontact with the interior of the first cased borehole to an electrodeattached to and in electrical contact with a portion of a secondborehole casing which is above the surface of the earth.

Method I-B (8): passing A.C. current from one or more electrodes inelectrical contact with the interior of the first cased borehole to oneor more electrodes attached to and in electrical contact with a portionof a second borehole casing which is above the surface of the earth.

Method I-B (9): passing A.C. current from one electrode in electricalcontact with the interior of the first cased borehole to an electrodeattached to and in electrical contact with the interior wall of a secondopen, or uncased, borehole.

Method I-B (10): passing A.C. current from one or more electrodes inelectrical contact with the interior of the first cased borehole to oneor more electrodes attached to and in electrical contact with theinterior wall of a second open, or uncased, borehole.

Method I-B (11): passing A.C. current from one electrode attached to andin electrical contact with the portion of the first borehole casingwhich protrudes above the surface of the earth to an electrode attachedto and in electrical contact with the portion of a second boreholecasing which protrudes above the surface of the earth.

Method I-B (12): passing A.C. current from one or more electrodesattached to and in electrical contact with the portion of the firstborehole casing which protrudes above the surface of the earth to one ormore electrodes attached to and in electrical contact with the portionof a second borehole casing which protrudes above the surface of theearth.

Method I-B (13): passing A.C. current from one electrode in electricalcontact with the portion of the first borehole casing which protrudesabove the surface of the earth to an electrode in electrical contactwith interior of a second borehole casing.

Method I-B (14): passing A.C. current from one or more electrodes inelectrical contact with the portion of the first borehole casing whichprotrudes above the surface of the earth to one or more electrodes inelectrical contact with the interior of a second borehole casing.

Method I-B (15): passing A.C. current from one electrode in electricalcontact with the portion of the first borehole casing which protrudesabove the surface of the earth to one electrode in electrical contactwith the interior of a second open, or uncased, borehole.

Method I-B (16): passing A.C. current from one or more electrodes inelectrical contact with the portion of the first borehole casing whichprotrudes above the surface of the earth to one or more electrodes inelectrical contact with the interior of a second open, or uncased,borehole.

Method I-B (17): passing A.C. current from one electrode in electricalcontact with the portion of the first borehole casing which protrudesabove the surface of the earth to one electrode in electrical contactwith the surface of the earth remote from said first borehole casing.

Method I-B (18): passing A.C. current from one or more electrodes inelectrical contact with the portion of the first borehole casing whichprotrudes above the surface of the earth to one or more electrodes inelectrical contact with the surface of the earth remote from said firstborehole casing.

Method I-B (19): passing A.C. current from one electrode in electricalcontact with any portion of the first borehole casing to two or moreelectrodes in electrical contact with any portions of two or moreboreholes which may be cased boreholes or open boreholes.

Method I-B (20): passing A.C. current from one or more electrodes inelectrical contact with any portion of the first borehole casing to twoor more electrodes in electrical contact with any portions of two ormore boreholes which may be cased boreholes or open boreholes.

Method I-B (21): while performing measurements of the longitudinalcomponents of the A.C. magnetic field inside the first borehole casing,passing current between an electrode in electrical contact with anyportion of a second borehole casing to an electrode in electricalcontact with any portion of a third borehole casing.

Method I-B (22): while performing measurements of the longitudinalcomponent of the A.C. magnetic field inside the first borehole casing,passing current between an electrode in electrical contact with anyportion of a second borehole casing to an electrode in electricalcontact with the surface of the earth.

Method I-B (23): while performing measurements of the longitudinalcomponent of the A.C. magnetic field inside the first borehole casing,passing current between an electrode in electrical contact with anyportion of a second borehole casing to an electrode in electricalcontact with any portion of a second open hole, or uncased, borehole.

Method I-B (24): while performing measurements of the longitudinalcomponent of the A.C. magnetic field inside the first borehole casing,passing current between an electrode in electrical contact with anyportion of a second borehole casing to two or more electrodes which maybe attached to two or more electrodes in electrical contact with casedboreholes, uncased boreholes, or the surface of the earth.

Method I-B (25): while performing measurements of the longitudinalcomponent of the A.C. magnetic field inside the first borehole casing,passing current between two or more electrodes which are in electricalcontact with the surface of the earth.

Still other methods of conducting current through formation are obvious,but this list is terminated here for the sake of brevity. For example,in all the Methods cited, one or more extra calibration sources can beused to calibrate said detectors which may be located inside the firstcased borehole, in another cased or open borehole, or on the surface ofthe earth. Furthermore, many additional methods may be devised whichalter from one measurement configuration to another thereby providing analternating measurement signal that in essence reveals differencesbetween one geological region and another. The point is that theinvention provides numerous methods for passing A.C. current throughformation which results in the production of many different typesprimary source fields.

Another useful detailed Procedure may be defined by the following:Method I-A, used in combination with Method II-A, used in combinationwith Method III-D, and used in combination with Method IV-B. Again,there are many ways to pass current through insulated wires as definedby Method I-A. Therefore, the following subcategories of Method I-A arelisted as follows:

Method I-A (1): conducting A.C. current through an insulated wire on thesurface of the earth which is circular and concentric with said firstcased borehole.

Method I-A (2): conducting A.C. current through an insulated wire on thesurface of the earth which is circular and which is not concentric withsaid first cased borehole;

Method I-A (3): conducting A.C. current alternatively through a firstinsulated circular wire on the surface of the earth which is concentricwith said first cased borehole and which has a first diameter, and thenthrough a second insulated circular wire on the surface of the earthwhich is concentric with said first cased borehole and which has asecond diameter.

Method I-A (4): conducting A.C. current alternatively through a firstinsulated circular wire on the surface of the earth which is concentricwith said first cased borehole and which has a first diameter, and thenthrough a second insulated circular wire on the surface of the earthwhich not concentric with said first cased borehole whose center islocated a distance from said first cased borehole and which has a seconddiameter.

Method I-A (5): conducting A.C. current through an insulated wire on thesurface of the earth which forms a rectangular array which is symmetricwith the position of said first borehole casing.

Method I-A (6): conducting A.C. current through an insulated wire on thesurface of the earth which forms a rectangular array where one side ofsaid rectangular array is much closer to said first borehole casing thansaid other remaining sides of the rectangular array.

Method I-A (7): conducting A.C. current through an insulated wire on thesurface of the earth which has any geometric shape and which may belocated at any distance from said first cased borehole.

Method I-A (8): conducting A.C. current through an insulatedsuperconducting wire on the surface of the earth which has any geometricshape and which may be located at any distance from said first casedborehole.

Method I-A (9): conducting A.C. current through a solenoid having an aircore which is placed at a specific distance of separation from the A.C.magnetic detector means in said first cased borehole.

Method I-A (10): conducting A.C. current through a solenoid having aferromagnetic core which is placed at a specific distance of separationfrom the detector means in the first cased borehole.

Method I-A (11): conducting A.C. current through a solenoid having anair core which is placed on the surface of the earth.

Method I-A (12): conducting A.C. current through a solenoid having aferromagnetic core which is placed on the surface of the earth.

Method I-A (13): while performing measurements with the detectorsensitive to the longitudinal component of the A.C. magnetic field inthe first cased borehole, conducting A.C. current through a solenoidwhich has an air core which is located inside a second cased borehole.

Method I-A (14): while performing measurements with the detectorsensitive to the longitudinal component of the A.C. magnetic field inthe first cased borehole, conducting A.C. current through a solenoidwhich has a ferromagnetic core which is located inside a second casedborehole.

Method I-A (15): while performing measurements with the detectorsensitive to the longitudinal component of the A.C. magnetic field inthe first cased borehole, conducting A.C. current through a solenoidwhich has an air core which is located inside a second open, or uncased,borehole.

Method I-A (16): while performing measurements with the detectorsensitive to the longitudinal component of the A.C. magnetic field inthe first cased borehole, conducting A.C. current through a solenoidwhich has a ferromagnetic core which is located inside a second open, oruncased, borehole.

Method I-A (17): while performing measurements with the detectorsensitive to the longitudinal component of the A.C. magnetic field inthe first cased borehole, conducting A.C. current alternatively firstthrough a first solenoid which has an air core located at a firstdistance above the detector means in said first cased borehole, and thenalternatively conducting A.C. current through a second solenoid whichhas an air core located at a second distance above the detector means insaid first cased borehole.

Method I-A (18): while performing measurements with the detectorsensitive to the longitudinal component of the A.C. magnetic field inthe first cased borehole, conducting A.C. current alternatively firstthrough a first solenoid which has a ferromagnetic core located a firstdistance above the detector means in said first borehole, and thenalternatively conducting A.C. current through a second solenoid whichhas a ferromagnetic core located at a second distance above the detectormeans in said first cased borehole.

Method I-A (19): while performing measurements with the detectorsensitive to the longitudinal component of the A.C. magnetic field inthe first cased borehole, conducting A.C. current alternatively firstthrough a first solenoid which has an air core located a first distanceabove the detector means in said first cased borehole, and thenalternatively conducting A.C. current through a second solenoid whichhas an air core located on the surface of the earth.

Method I-A (20): while performing measurements with the detectorsensitive to the longitudinal component of the A.C. magnetic field inthe first cased borehole, conducting A.C. current alternatively firstthrough a first solenoid which has a ferromagnetic core located a firstdistance above the detector means in said first cased borehole, and thenalternatively conducting A.C. current through a second solenoid whichhas a ferromagnetic core located on the surface of the earth.

Method I-A (21): while performing measurements with the detectorsensitive to the longitudinal component of the A.C. magnetic field inthe first cased borehole, conducing A.C. current alternatively firstthrough an insulated circular shaped wire on the surface of the earthdisposed symmetrically around the first cased borehole, and thenconducting A.C. current through a solenoid with an air core locatedinside a second borehole casing.

Method I-A (22): while performing measurements with the detectorsensitive to the longitudinal component of the A.C. magnetic field inthe first cased borehole, conducing A.C. current alternatively firstthrough an insulated circular shaped wire on the surface of the earthdisposed symmetrically around the first cased borehole, and thenconducting A.C. current through a solenoid with a ferromagnetic corelocated inside a second cased hole.

Method I-A (23): while performing measurements with the detectorsensitive to the longitudinal component of the A.C. magnetic field inthe first cased borehole, conducting A.C. current alternatively firstthrough a first solenoid with an air core which is located at a firstvertical position within a second cased borehole, and then conductingA.C. current through a second solenoid with an air core which is locatedat a second vertical position within said second cased borehole.

Method I-A (24): while performing measurements with the detectorsensitive to the longitudinal component of the A.C. magnetic field inthe first cased borehole, conducting A.C. current alternatively firstthrough a first solenoid with a ferromagnetic core which is located at afirst vertical position within a second cased borehole, and thenconducting A.C. current through a second solenoid with a ferromagneticcore which is located at a second vertical position within said secondcased borehole.

Still other methods are obvious for conducting current through insulatedwires located in various parts of an oil field, but this list isterminated here for the sake of brevity. For example, in all the Methodscited, one or more extra calibration sources can be used to calibratesaid detectors which may be located inside the first cased borehole, inanother cased or open borehole, or on the surface of the earth.Furthermore, many additional methods may be devised which alter from onemeasurement configuration to another thereby providing an alternatingmeasurement signal that in essence reveals differences between onegeological region and another. An example of such an alternativemeasurement technique is described in Method I-A (4), but there existmany variations on that basic idea. The point is that the inventionprovides for a wide variety of methods for conducting A.C. currentthrough insulated wires which result the production of many differentprimary source fields.

It should be restated here that the invention provides for an enormousnumber of different Procedures. These different Procedures can be listedas follows:

Method I-A (1), or I-A(2), . . . , or I-A(24), or Method I-B(1), or I-B(2), . . . , I-B (25);

In combination with Method II-A, or II-B, or II-C, or II-D, or II-E, orII-F, or II-G, or II-H, or II-I;

In combination with Method III-A, or III-B, or III-C, or III-D, orIII-E, or III-F;

In combination with Method IV-A or IV-B.

For example, the invention shown in FIG. 1 can be described by thefollowing Procedure: Method I-A (18); in combination with Method II-C;in combination with Method III-D; in combination with either Method IV-Aor Method IV-B.

Similarly, FIG. 5 can be described by the following Procedure: MethodI-B (1); in combination with Method II-C; in combination with MethodIII-B; in combination with either Method IV-A or Method IV-B.

And finally, FIG. 6 can be described by the following Procedure: MethodI-A (3); since it was not specified, either Methods II-A, II-B, II-C orII-D; in combination with Method III-D; in combination with eitherMethod IV-A or Method IV-B.

To select the ideal Procedure for a given problem in an oil field, thefollowing generalities should be noted. The response of a magneticgradiometer is related to its overall dimensions. For example, agradiometer whose sensors are separated by 5 meters will probably have asensitivity to geophysical properties up to approximately 5 meters awayfrom the gradiometer. On the other hand, a single magnetic detector isresponsive to fields generated great distances away. Therefore, a singlesensor is sensitive to fields generated at great distances whereas agradiometer is sensitive to local changes in fields.

Therefore, to measure resistivity changes in geological formationsimmediately adjacent to a cased borehole, a gradiometer is naturally tobe used as shown explicitly in FIGS. 1, 4, 5, and 6.

It is also stated in the text however, that the inventions shown inFIGS. 1, 4, 5 and 6 can also be operated in a mode where only one singlesensor is used (the other sensors in the gradiometer are therefore notused, or disconnected). In this case, the embodiments used in thismanner are sensitive to geological formations relatively distant fromthe cased hole.

In addition, the invention clearly provides for the measurement of theaverage resistivity of large portions of an oil reservoir. For exampleconsider FIG. 7 which embodies the following Procedures: Method I-A (4);in combination with Method II-A; in combination with Method III-A; incombination with Method IV-B. It should be noted that FIG. 7 is verysimilar to FIG. 6 in that all the numbered elements are the same. InFIG. 6, circular insulated wire 82 is concentric with the first casedborehole and is located on the surface of the earth. In FIG. 7, circularinsulated wire 82 has been moved to a position where the center of saidcircle P is a distance X away from the first cased borehole. Initially,wire 80 is energized with A.C. current. When wire 82 is alternativelyenergized, then the changes observed are related to the resistivity inregion R and the distance of separation between the detector and pointP.

Fields generated by the circular wire 82 decrease in depth Z andposition X from the first cased borehole. The A.C. magnetic fieldsgenerated will attenuate along the distance ζ which is the distance ofinvestigation along a line from point P to point Q, the center of thesensor in the first cased borehole. In the simplest of approximations,it is first assumed that no earth is present and the vector magneticfield generated by the circular wire is given by B_(o) (X, Z, ε) where εis the azimuthal position shown in FIG. 7. (The A.C. magnetic field fromsaid circular loop in the absence of the earth is to be calculated fromConcepts in Electricity and Magnetism, Reuben Benumof, Holt, Rinehartand Winston, N.Y., 1961, Equation 10.1, page 164). In addition, theconductive nature of the earth also attenuates said A.C. fields. Anexact calculation of the fields according to Fields and Waves inCommunication Electronics, op. cit., Equations 5, 6, and 7 on page 149,subject to boundary conditions, provides a detailed solution. Muchtheoretical work on this subject is also provided in Frequency andTransient Soundings, by Alexander A. Kaufman and George V. Keller,Elsevier, N.Y., 1983, particularly in Chapters 1, 3, 5 and 7. Thereforethe exact A.C. magnetic field may be obtained from assumed geophysicalproperties which is B(X,Z,ε). However, a first simple approximation tothe exact solution which basically shows how the invention works isgiven by an exponentially attenuated magnetic field as follows:

    B(X,Z,ε)=B.sub.o (X,Z,ε)e.sup.-ζ/δEq. 2

Here, δ is given by Eq. 1. Therefore, detector 74 measures the responseto alternatively applied fields from wire 80 and then 82 for severaldifferent frequencies between 0.001 Hz and 20 Hz, and then said data isrepeatedly acquired at many different vertical positions Z. By measuringthe departure of the measured A.C. magnetic fields with detector 74 fromthe theoretically predicted values without the conductive earth beingpresent provides information concerning regions such as R shown in FIG.7. The calibration coil 84 is used to determine the average response ofthe sensor 74 to calibration fields at different frequencies which canbe used to determine the influence of the actual casing present on theresponse of the detector 74. Therefore, methods and apparatus have beendescribed which measure geological formation properties great distancesaway from said first cased borehole.

Another embodiment of the invention is shown in FIG. 8 which alsoprovides for measurements of the average resistivity of large portionsof an oil reservoir. The invention is shown in FIG. 8 which requires thefollowing Procedure: Method I-A (13); in combination with Method II-A;in combination with Method III-A; in combination with Method IV-B.

Most of the elements have already been described in FIG. 8 including thelongitudinal A.C. magnetic field detector 74. However, another casedborehole 88 is present in the oil field, and an air core solenoid 90 issuitably energized by the power amplifier 22. It is evident that in sucha geometry, the average resistivity of the region R' affects themagnitude of the longitudinal A.C. magnetic field seen inside cased hole10. There are many ways to take data here effectively. One method is asfollows. For a given vertical position of source 90, measure theresponse of longitudinal detector 74 at many different verticalpositions. Then change the position of source 90 and measure theresponse of longitudinal detector 74 at many different verticalpositions. After this process is repeated several times, sufficient datais obtained to infer the average resistivity of regions such as R' shownin FIG. 8.

And finally, FIG. 9 shows another embodiment of the invention. Themethod used here may be succinctly described as follows: Method I-B(13); in combination with II-A; in combination with Method III-A; incombination with Method IV-B. Here, almost all of the elements havealready been defined. In addition, the power amplifier in thisembodiment conducts current from an electrode 92 in electrical contactwith the portion of the first borehole casing protruding from thesurface of the earth to an electrode 94 which is in electrical contactwith the interior of the second cased borehole. The surface of the earth96 is shown here for clarity. Clearly, the size of the longitudinal A.C.magnetic field measured by 74 is dependent upon the relative resistivityof various formations between the cased holes shown respectively as ρ₁,ρ₂, and ρ₃ in FIG. 9.

In this particular example, and in others, it is generally true ofcourse that the measured longitudinal component of the A.C. magneticfield inside the cased well is due to the vector sum of the primarysource of exciting A.C. magnetic fields and the resulting secondary A.C.magnetic fields generated by the presence of the casing and by thepresence of the geological formations.

It should be noted that phase sensitive detector 58 in FIG. 9 has anin-phase output and an out-of-phase output. These in-phase andout-of-phase outputs were already briefly defined in the text of thedescription of element 58 in FIG. 1, and they are explicitly shown as"I" and "O" respectively in element 58 in FIG. 1. (Element No. 58 inFIGS. 1, 5, 6, 7, 8, and 9 all have an in-phase output "I", and anout-of-phase output "O", even if these outputs are not explicitly shownon the drawings). An example of such a phase sensitive detector is theModel "5204 Lock-In Analyzer" manufactured by EG&G Princeton AppliedResearch Corporation located in Princeton, N.J., which possesses anin-phase output and an out-of-phase output incorporated into oneinstrument.

Referring again to FIG. 9, using standard experimental instrumentationand techniques used with phase sensitive detection equipment, the"in-phase part" of the longitudinal component of the A.C. magnetic fielddetected with sensor 74 can be measured. That "in-phase part" of thelongitudinal component of the A.C. magnetic field is defined as thatpart of the A.C. magnetic field which is in-phase with the A.C. currentconducted through formation from power amplifier 22. For example,supposed that the A.C. current conducted into the formation from poweramplifier 22 has a time dependence described mathematically in time ascos(wt), where "cos" is the cosine function, w is the angular frequency,and t is the time. Then the part of the longitudinal component of theA.C. magnetic field detected with sensor 74 which also has the timedependence of cos(wt) is defined as the "in-phase part" of thelongitudinal component of the A.C. magnetic field. Similarly, the partof the longitudinal component of the A.C. magnetic field detected withsensor 74 which instead has the time dependence of sin(wt) is defined asthe "out-of-phase part" of the longitudinal component of the A.C.magnetic field, where "sin" is the sine function.

Therefore, in FIG. 9, the phrases "in-phase part" and "out-of-phasepart" are defined in relation to the phase of the A.C. current conductedinto formation. In general, the "in-phase part" is defined herein asthat part of the measured longitudinal component of the A.C. magneticfield which is in-phase with the conducted A.C. current that isresponsible for generating the measured A.C. magnetic field. In the caseof FIG. 9, the A.C. current generating the longitudinal component of theA.C. magnetic field is that A.C. current caused to flow through thegeological formation. In FIG. 1, the A.C. current generating thelongitudinal component of the A.C. magnetic field to be measured is thatA.C. current flowing through wire 26 alternatively to magnetic sourcesS1 or S2. Convenient methods of producing A.C. magnetic fields are infact different methods of causing A.C. currents to flow in different"circuit pathways" which may, or may not, include A.C. current flowthrough geological formations as discussed above. Furthermore,conducting A.C. current through a particular "circuit pathway" providesa particular means to subject a cased well to a subterranean A.C.magnetic field. Again such means can include passing A.C. currentsthrough any number of "circuit pathways" including all those individual"circuit pathways" described as Methods I-A (1) through I-A (24) andMethods I-B (1) through I-B (25) that have already been described indetail.

"In-phase parts" and "out-of-phase parts" of waveforms are used tointerpret data measured with induction coils in open holes, and suchinformation is used to interpret geophysical information related to thesurrounding geological formations in those uncased wells. By analogytherefore, several preferred embodiments of this invention teachmeasuring the "in-phase parts" and the "out-of-phase parts" of thelongitudinal components of A.C. magnetic fields within cased wells todetermine geophysical properties of the adjacent geological formations.

It should also be noted that there is an equivalent mathematical way todescribe the "in-phase parts" and the "out-of-phase parts" of thelongitudinal components of the A.C. magnetic fields. Using standardvector analysis, these two components can be alternatively representedas an the corresponding "amplitude" and the corresponding "phase angle"of the measurements described as follows. Using standard vectoranalysis, the "in-phase part" and the "out-of-phase part" of a givenmeasurement are represented as orthogonal components along the abscissaand the ordinate of an ordinary 2 dimensional graph which thereforedefines a given point on that graph. Alternatively, and equivalently,this point on the graph can be represented by an "amplitude" (which isthe square root of the sums of the squares of the "in-phase components"and the "out-of-phase components"), and an angle from the abscissa,which is defined as "the phase angle" herein. Therefore, severalpreferred embodiments of the invention provide for methods and apparatusfor measuring "the amplitudes" and "the phase angles" of thelongitudinal components of the A.C. magnetic fields measured withincased wells to determine geophysical properties of adjacent geologicalformations. At any given vertical position within a well using a chosenembodiment of the invention, "the amplitude" and "the phase angle" ofthe longitudinal component of the A.C. magnetic field is measured withinthe cased well in response to A.C. currents caused to flow in a chosen"circuit pathway" to determine geophysical properties of the adjacentgeological formations.

The invention employs various types of calibration means to compensatefor thickness variations of the casing. For example, calibrating coils49 and 50 in FIG. 1 are used calibrate for thickness variations of thecasing as stated on page 11 lines 24-26. Calibration coil 63 in FIG. 4is used for the same purpose (see page 16, lines 6-7). Calibration coils84 and 86 in FIG. 6 are also used for the same purpose as described indetail on page 18 lines 15-24.

In the case of FIG. 6, a total of three magnetic sensing means are usedto measure the longitudinal components of A.C. magnetic fields downholewithin the cased well. Calibration coil 84 is used to perform at leastone additional first calibration step to provide first independentinformation at least partially responsive to the thickness of the casingto compensate measurements for the thickness variations of the casing.In the embodiment shown in FIG. 6, the independent first information soobtained is most responsive to the thickness of the casing adjacent tolongitudinal detectors 74-76. Calibration coil 86 is used to provide asecond independent calibration step to provide second independentinformation at least partially responsive to the thickness of the casingto further compensate measured longitudinal components for the thicknessvariations of the casing. In the embodiment shown in FIG. 6, theindependent second information so obtained is most responsive to thethickness of the casing adjacent to longitudinal detectors 76-78.Consequently, the invention provides one or more compensation steps tocompensate for thickness variations of the casing. Of course, theinvention provides the necessary apparatus to implement the methods ofoperation described herein.

The length of the casing adjacent to longitudinal A.C. magnetic fielddetectors 74-76 is L₁ and the resistance in ohms of the casing alongthat length is R₁. The length of the casing adjacent to longitudinalA.C. magnetic field detectors 76-78 is L₂ and the resistance of thecasing along that length is R₂. Therefore, the average resistance perlength adjacent to detectors 74-76 is r₁ =R₁ /L₁. Further, the averageresistance per length adjacent to detectors 76-78 is r₂ =R₂ /L₂.Therefore, the calibration coils 84 and 86 are used respectively in FIG.6 to compensate for the respective different resistances per unit lengthdefined as r₁ and r₂. Similar comments may be made concerning the othercalibration coils described above for other embodiments of theinvention. See for example page 11, lines 24-26, regarding FIG. 1.

And furthermore, the high precision A.C. magnetic gradiometer previouslydescribed was explicitly deigned to work inside conductive and magneticsteel borehole casing. However, it will respond slightly better if it isnot surrounded by borehole casing. Therefore, the high precision A.C.magnetic gradiometer may be used in other geophysical exploration workinside uncased holes. It is very useful for uncased holes because in theprior art, no practical devices have been constructed which measure A.C.magnetic fields to a sensitivity of 1×10⁻¹⁰ gauss peak-to-peak atfrequencies between 1 and 10 Hz with integration times of severalseconds in the presence of much larger geomagnetic noise. In particular,current sources can be placed in one open borehole causing resultingA.C. magnetic fields which depend on the preferential A.C. current flowthrough relatively conductive formations and the precision A.C. magneticgradiometer can be placed in another open borehole. Precision inductionmeasurements can then be performed which yield properties of therelatively conductive formations.

While the above description contains many specificities, there shouldnot be construed as limitations on the scope of the invention, butrather as exemplification of one preferred embodiment thereof. As hadbeen briefly described, there are many possible variations. Accordingly,the scope of the invention should be determined not only by theembodiments illustrated, but by the appended claims and their legalequivalents.

I claim:
 1. The method of measurement of geological formation propertiesthrough conductive and magnetic steel borehole casing which comprisesthe steps of applying a primary A.C. magnetic field to the subterraneanformation from a magnetic means located on the surface of the earthwherein the frequency of the applied A.C. magnetic field is between0.001 Hz and 20 Hz which penetrates the formation to the depth ofmeasurement thereby resulting in the production of eddy currents in thegeological formation which in turn produce secondary A.C. magneticfields which have longitudinal components at the casing whichsubsequently penetrate the casing to the interior of the casing,measuring the longitudinal components of said primary and said secondaryA.C. magnetic fields on the interior of the casing, and performing atleast one additional first calibration step to provide first independentinformation at least partially responsive to the thickness of the casingto compensate said measurements for the thickness variations of thecasing, repetitively performing said measurements and each firstcalibration steps at many vertical positions within the borehole casingand determining from said measured longitudinal components and saidcalibration steps characteristic parameters for the formation throughsaid borehole casing including the resistivity and changes in theresistivity of the geological formation.
 2. The method as defined inclaim 1 wherein following each first calibration step is a secondindependent calibration step at each vertical position within the casingto provide second independent information at least partially responsiveto the thickness of the casing to further compensate said measuredlongitudinal components for the thickness variations of the casing. 3.An apparatus for measurement of geological formation properties throughconductive and magnetic steel borehole casing comprising at least oneprimary source of exciting A.C. magnetic fields on the surface of theearth, the frequency of the exciting A.C. fields being chosen to subjectthe subterranean formation to the exciting A.C. magnetic fields therebyresulting in the production of eddy currents in the formation whichsubsequently produce secondary A.C. magnetic fields characteristic ofthe formation whereby the longitudinal and azimuthal components of saidsecondary A.C. magnetic fields penetrate the wall of the casing to theinterior of the borehole casing, in combination with one or moremagnetic field sensing means positioned inside the borehole casingresponsive to the longitudinal components of said primary and secondaryA.C. magnetic fields, in combination with at least a first calibrationmeans to calibrate said magnetic field sensing means which is at leastpartially responsive to thickness variations in the casing, thefrequency of the source of A.C. magnetic fields on the surface of theearth being between 0.001 Hz and 20 Hz thereby allowing said A.C.magnetic fields to penetrate the earth to great depths which causes eddycurrents to flow in the geological formation which causes the subsequentgeneration of secondary A.C. magnetic fields at the same frequency whichtherefore penetrate the walls of the conductive and magnetic boreholecasing whereby the longitudinal components of said primary and secondaryA.C. magnetic fields are measured thereby providing characteristicformation properties including the resistivity of the geologicalformation.
 4. The apparatus defined in claim 3 having a secondindependent calibration means to further calibrate said magnetic fieldsensing means which is at least partially responsive to thicknessvariations in the casing.
 5. The method of measurement of geologicalformation properties penetrated by a conductive and magnetic steelborehole casing which comprises the steps of conducting A.C. currentthrough an insulated current conducting wire on the surface of the earthwherein the frequency of the current is between 0.001 Hz and 20 Hz whichtherefore generates and applies a primary A.C. magnetic field to thesubterranean formation to the depth of measurement thereby resulting inthe production of eddy currents in the geological formation which inturn produce secondary A.C. magnetic fields which cause A.C. magneticfields which have longitudinal components at the casing whichsubsequently penetrate the casing to the interior of the casing,measuring the longitudinal components of said primary and said secondaryA.C. magnetic fields on the interior of the casing, and performing atleast one additional first calibration step to provide first independentinformation at least partially responsive to the thickness of the casingto compensate said measurements for the thickness variations of thecasing, repetitively performing said measurements and said calibrationsteps at many vertical positions within the borehole casing anddetermining from said measured longitudinal components and saidcalibration steps characteristic parameters for the formation throughsaid borehole casing including the resistivity and changes in theresistivity of the geological formations.
 6. The method as defined inclaim 5 wherein following each first calibration step is a secondindependent calibration step at each vertical position within the casingto provide second independent information at least partially responsiveto the thickness of the casing to further compensate said measuredlongitudinal components for the thickness variations of the casing. 7.The apparatus for measuring subterranean properties of geologicalformations penetrated by a conductive and magnetic steel borehole casingcomprising a circular loop of insulated wire concentric with saidborehole casing which is energized with A.C. current with a magnitude inexcess of 0.10 amps peak-to-peak at a frequency within the frequencyinterval of 0.001 Hz to 20 Hz which therefore subjects the subterraneanformation to an applied primary A.C. magnetic field thereby resulting inthe production of eddy currents which in turn produce secondary A.C.magnetic fields responsive to the resistivity of the subterraneangeological formation, in combination with one or more longitudinal A.C.magnetic field detector means located at one or more depths from thesurface of the earth within said cased borehole which are responsive tothe longitudinal components of said primary and secondary fields whichpenetrate said casing at said depths, in combination with at least afirst calibration means to calibrate one or more of the magnetic fieldsensing means which is at least partially responsive to thicknessvariations in the casing, which thereby provides an apparatus capable ofmeasuring information useful for determining the resistivity and changesin the resistivity of subterranean geological formations in the vicinityof said cased borehole.
 8. The apparatus defined in claim 7 having asecond independent calibration means to further independently calibrateone or more of the magnetic field sensing means which is at leastpartially responsive to thickness variations in the casing.